Vol. 4, No. 4, 2010

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Algebraic properties of generic tropical varieties

Tim Römer and Kirsten Schmitz

Vol. 4 (2010), No. 4, 465–491
Abstract

We show that the algebraic invariants multiplicity and depth of the quotient ring SI of a polynomial ring S and a graded ideal I S are closely connected to the fan structure of the generic tropical variety of I in the constant coefficient case. Generically the multiplicity of SI is shown to correspond directly to a natural definition of multiplicity of cones of tropical varieties. Moreover, we can recover information on the depth of SI from the fan structure of the generic tropical variety of I if the depth is known to be greater than 0. In particular, in this case we can see if SI is Cohen–Macaulay or almost-Cohen–Macaulay from the generic tropical variety of I.

Keywords
tropical variety, constant coefficient case, Gröbner fan, generic initial ideals, Cohen–Macaulay, multiplicity, depth
Mathematical Subject Classification 2000
Primary: 13F20
Secondary: 14Q99, 13P10
Milestones
Received: 11 September 2009
Revised: 5 February 2010
Accepted: 6 April 2010
Published: 13 June 2010
Authors
Tim Römer
Institut für Mathematik
Universität Osnabrück
49069 Osnabrück
Germany
Kirsten Schmitz
Institut für Mathematik
Universität Osnabrück
49069 Osnabrück
Germany